The present invention relates to a technique adapted to perform accurate measurements of the metallic and dielectric properties of materials at microwave frequencies; and more particularly, to an apparatus and method for determining the absolute screening length (or penetration depth) and surface resistance of metals or superconductors, either films or bulk, absolute complex conductivity and surface impedance of metals and superconductors, as well as for determination of dielectric constants and loss tangent of gases and liquids.
The present invention further relates to a technique using a resonant structure formed of a pair of substantially identical samples under investigation which are positioned in substantially parallel relationship each with respect to the other having a dielectric spacer of variable thickness disposed between the samples. The resonant frequency and quality factor vs. the variable thickness of the dielectric spacer are measured to be inserted in predetermined mathematical formulas correlated to the type of the samples in order to extract the absolute values of penetration depths and surface resistance for the samples. Extracted values of penetration depths and surface resistance are further used for determination of absolute complex conductivity and surface impedance of metals and superconductors in both films and bulk materials.
Investigation of the microwave surface impedance ZS=RS+iXS of superconductors has been given prominence. Much of such prior investigations has been based on the pioneering works of Pippard and has been invigorated by the discovery of high temperature superconductors (HTS). An additional impetus for the development has been the appearance of a new family of synthesized microwave sources and network analyzers which has enabled a number of techniques to be developed.
Most of these techniques provide accurate determinations of the absolute value of the surface resistance, RS, and provide sensitive measurements of changes in the surface reactance XS=xcexc0xcfx89xcex or the magnetic penetration depth xcex. However, there still exists the problem of experimentally determining the absolute value of xcex since it is small, possibly on the order of tens to hundreds of nanometers. In fact, unlike RS measurements, there is no well-established universal and commonly accepted technique for determining the absolute penetration depth in superconductors.
Investigation of superconducting surface impedance is important since it yields valuable information about intrinsic (charge carrier density, pairing state symmetry, quasiparticle excitation spectrum and relaxation time) and extrinsic properties (microstructure) of the specimen under study. These properties can be deduced from the surface impedance ZS={square root over (ixcexc0+L xcfx89/"sgr")} (local limit) measured as a function of temperature, applied magnetic field, doping, or impurity concentration, wherein xcexc0 is a constant of permeability of free space, and xcfx89 is an angular frequency of the field. The complex conductivity, "sgr"="sgr"1xe2x88x92i"sgr"2, is a fundamental quantity which theories of superconductivity are able to calculate. However, the inability to determine both the surface resistance and the absolute value of xcex for the same sample often hampers effort to construct the complex conductivity from the surface impedance data. For example, the real part of the conductivity "sgr"1 can be extracted from RS only if the absolute xcex is available.
The appearance of low loss HTS epitaxial thin films on single crystal dielectric substrates has led to a growing field of superconducting wireless communication. In this respect, knowledge of the surface impedance is important to obtain the optimum performance of superconducting RF/microwave components and circuits. Another important issue is the establishment of a standard characterization technique for HTS thin films for microwave applications.
Existing experimental techniques suitable for measurement of absolute xcex in superconductive thin films and single crystals may be divided into the following four categories: absolute length scale techniques, reflection or transmission measurements of electromagnetic fields (mutual inductance, microwave/millimeter wave, infrared (IR) spectroscopy), measurement of internal magnetic field distribution (muon spin rotation [xcexcSR], neutron scattering), and Josephson tunneling experiments. Each of these techniques will be described in the following paragraphs.
1. Absolute Length Scale Techniques
An optimum way to measure an absolute screening length in a superconducting (or normal metal) sample is to determine an absolute length scale, l, which is comparable to and directly linked to the absolute value of xcex. Many of the existing techniques for measuring changes in xcex measure a signal proportional to the value of lxe2x88x92xcex, hence the greater the xcex/l ratio, the higher the sensitivity to the penetration depth. However, little effort has been made to measure an absolute xcex via determination of an absolute length scale due to the fact that in practice, the latter cannot be measured with sufficient accuracy.
The absolute length scale techniques are generally based on the effect of electromagnetic field exclusion in the Meissner state of a superconductor. For single crystals these include DC/AC magnetometry and RF/microwave resonator perturbation techniques. In all of them l is the specimen""s linear dimension and the measured signal (for example, shift in the resonant frequency between the empty and perturbed resonator) is proportional to (lxe2x88x92xcex3xcex)xc3x97(area of the sample), where xcex3xcx9cl depends upon the sample geometry and the field configuration. Usually, for crystals xcex/lxcx9c10xe2x88x923-10xe2x88x924 and the relevant calibration does not allow measurement of an absolute xcex.
In the case of a resonator in which all or a substantial part of it is made up of the superconductive material, l=xcex93/xcexc0xcfx89, where xcex93 is the resonator geometrical factor. The resonant frequency is fSC≈f0(lxe2x88x92xcex/2l), where f0 is the frequency of the same perfectly conducting resonator. Cavity-like resonators, such as end-plates or dielectric resonators have l on the order of the wavelength of electromagnetic radiation and the ratio xcex/lxe2x89xa610xe2x88x924 is generally small.
Planar resonators, such as stripline or conventional parallel plates, carry a slowed-down electromagnetic wave with a phase velocity cSW=c/{square root over (∈eff+L (1+2+L xcex/s))}, where c is velocity of light in vacuum, ∈eff is the effective dielectric constant of the transmission line, and s is the dielectric thickness. Each have a high sensitivity to the penetration depth (down to 0.1 nm), since xcex/l=2xcex/sxcx9c10xe2x88x922-10xe2x88x924 in this case. However, neither the cavity-like nor planar resonators are suitable for direct measurement of absolute xcex (except possibly for the coplanar resonator), and only changes in xcex may be extracted from the experiment.
The most common way to evaluate an absolute xcex(T=0) using the above techniques involves fitting of the measured temperature dependence of the parameter relevant to the changes in xcex (commonly, shift in the resonant frequency) to a theoretical dependence for xcex(T) (a proper electrodynamic description of the experimental structure is required). Usually, this procedure works adequately for conventional superconductors where appropriate models (two fluid or BCS) for xcex(T) are well established. However, such models fail in the presence of extrinsic effects in the sample under study. In the case of HTS there is a lack of suitable models for xcex(T), and usually the absolute xcex values deduced from experiment are strongly dependent (up to 50%) on the form of the temperature model assumed.
The other three categories of techniques generally allow one to measure absolute xcex without the need to determine the absolute length scale. When combined with techniques of measuring the surface impedance, they allow reconstruction of the complex conductivity "sgr". However, it is most desirable to carry out the measurements of absolute xcex and RS within the same experimental arrangement and on the same sample.
2. Reflection/transmission of Electromagnetic Field
The mutual inductance technique is the most simple and accurate (to within a few percent) way to determine the penetration depth of thin films at low frequencies. It is based on the measurement of the mutual AC inductance of two axially symmetric coils separated by a superconducting film. This technique is usable for film thickness up to 1 xcexcm for typical (xcexxcx9c300 nm, sample linear size is 12 mm by 12 mm) HTS films. An accurate knowledge of the film thickness and its uniformity are required over the entire sample.
Microwave/millimeter wave reflection/transmission techniques are based on a measurement of S-parameters of a coaxial or cylindrical waveguide terminated by the superconductive sample (thin film). The absolute value of the reflection coefficient is close to unity and does not allow reliable measurement of absolute xcex. The transmission coefficient is  less than  less than 1 even for very thin films (down to dxcx9cxcexXS/Z0), hence the absolute version of this method requires sophisticated calibration (Z0 is the characteristic impedance of free space).
This problem can be eliminated in the case of relative transmission measurements, which in turn requires accurate knowledge of the sample normal state resistivity. Another typical complication for both methods is leakage of radiation around the sample. The transmission methods are generally limited to very thin films of homogeneous thickness.
In IR spectroscopy a Kramers-Kronig transform of the power reflectivity, measured over a wide range of frequency allows one to obtain "sgr"2 (xcfx89). The latter when extrapolated to the low-frequency limit "sgr"2(xcfx89≈0)=l/xcexc0xcfx89xcex2, provides the penetration depth. Alternatively the oscillator strength sum rule may be employed to obtain the strength of the zero frequency delta function response of the superconducting condensate. This technique has the advantage of working with very small samples (single crystals), and allows estimate of all three components of the penetration depth in anisotropic superconductors. However, this technique is very demanding technically and subject to uncertainty due to the finite frequency measurement range.
3. Probing of Internal Magnetic Field Distribution
The muon spin rotation/relaxation (xcexcSR) technique is a powerful tool to determine the local magnetic field distribution in a superconductor. This technique has the advantage of providing bulk measurement of xcex, but requires a detailed model of the superconducting mixed state.
Polarized neutron reflectometry (PNR) is based on the study of polarized neutron glancing angle reflection from the sample surface, which is sensitive to the screening of the external magnetic field inside a superconductor. Its advantage is sensitivity to the shape of the magnetic flux penetration profile itself, rather than just the penetrated magnetic flux. PNR has measured the absolute penetration depth in conventional superconductors (Nb). However, even for the best epitaxial HTS films available the overall surface topology is too poor to obtain xcex with sufficient precision.
4. Josephson Tunneling
The Josephson tunneling technique is based on modulation of the Josephson junction critical current by external magnetic field, and provides an accurate estimation of absolute xcex. Its main limitation is requirement that a Josephson junction be made with the material of interest.
It is clear from the aforesaid that it would be highly desirable to have a technique for accurate determination of the absolute values of xcex and RS, as well as absolute complex conductivity, surface impedance, and other parameters of metals and superconductors, free of the shortcomings of the prior methodologies and systems.
An object of the present invention is to provide a universal technique which can measure both the surface resistance and absolute value of the penetration depths in superconducting films, as well as the skin depth of normal metal using a variable spacing parallel plate resonator (VSPPR).
It is a further object of the present invention to provide a fully automated system for accurate measurements of metallic and dielectric properties of material at microwave frequencies both at room and cryogenic temperature.
It is still another object of the present invention to provide a technique in which a two-conductor electromagnetic resonant structure is formed of two identical samples separated by a dielectric spacer (which may be either liquid nitrogen, liquid helium, or vacuum), where one of the samples is displaced with respect to the other to vary the distance therebetween. During this displacement which is made in small increments, measurements of resonant frequency and the quality factor vs. the variable thickness of the dielectrical spacer are made. These measurements are further processed by inserting the measured values into mathematical formulae correlated with the type of the samples in order to extract therefrom absolute values of penetration depths and surface resistance for the samples which are further used for determining various metallic and dielectrical properties of materials under investigation.
It is another object of the present invention to provide a unique displacement mechanism for the resonant structure formed of a pair of identical samples separated by a dielectric spacer which has practically unlimited resolution and substantially zero friction between the structure elements.
It is still a further object of the present invention to provide a technique for measuring the penetration depth and surface resistance of superconducting and metallic materials for both films and bulk in which a parallelism of the samples forming a resonant structure is achieved and maintained by means of flexible coupling mechanism by bringing the samples into intimate contact therebetween for self-aligning which obviates the need for glue or other adhesive.
The technique of the present invention is designed specifically to determine the absolute screening length (or penetration depth) and the absolute surface resistance of a metal (or superconductor) film or bulk material at microwave frequencies. These two quantities are further combined to determine the absolute complex conductivity and surface impedance of the material. The invention can also be used to determine the dielectric constant and loss of tangent of gases and liquids at microwave frequencies.
For this purpose, a resonator is formed by two parallel metallic or superconducting plates (bulk material or thin films on dielectric substrates) separated by a thin dielectric spacer forming an open ended transmission line resonator. An important concept of the technique of the present invention is to measure the resonant frequency, f, and the quality factor, Q, of the VSPPR versus the continuously variable thickness of the dielectric spacer, and to fit the measured data into theoretical forms in order to extract the absolute values of xcex and RS therefrom.
The measurements are carried out using two nominally identical samples with flat face surfacexe2x80x94film and/or bulk metal and/or superconductor. The samples are positioned face-to-face to sandwich a thin dielectric separation (dielectric spacer) of variable thickness from 0 to 200 xcexcm. The material filling the dielectric spacer may include liquid nitrogen, liquid helium, vacuum, or other liquid or gas. The dielectric properties of the dielectric spacer are not necessarily known. This combination forms a 2-conductor parallel plate transmission line resonatorxe2x80x94Variable Parallel Plate Resonator (VPPR) which carries a quasi-TEM electromagnetic wave.
The Q-factor and resonant frequency of the resonator are dictated by its geometry, as well as by the ratio between the dielectric spacer thickness and the screening (penetration) depth in the samples. The losses in the resonator are determined by dielectric loss in the dielectric spacer matter, radiation losses, and the surface resistance of the samples. The first two contributions may be measured directly using a calibration procedure and/or eliminated by using disc-shape resonator with TM00i (where i is an integer) mode and vacuum dielectric spacer. The measured Q-factors can be corrected to reflect only the contribution of the surface resistance losses.
Accurate estimation of the absolute value of the penetration depth and surface resistance is based on the simultaneous analysis of spacer thickness dependencies of the resonator frequency f and the Ohmic quality factor O in association with the electrodynamics theory of the resonator.
The apparatus for measurements includes the Cryogenic Slider, Linear Actuator, Film Aligner and Microwave Coupling Probes.
The Cryogenic Slider is made from two coaxial thin-wall stainless steel tubes with the flexure-type bearings incorporated between the inner and outer tubes at both the top and bottom ends of the slider. One of the tubes, such as the outer tube, is fixed, while the other tube, such as the inner one, translates along the vertical axis driven by the Linear Actuator connected to the top of the slider. Bearings of special shape are made from Cu/Be foil and work either at room or at cryogenic temperature. They provide 1-mm of full travel while substantially reducing friction and theoretically giving resolution limited only by thermal fluctuations. The top of the slider is maintained at room temperature; the bottom is maintained at cryogenic conditions (4÷77 K). To compensate for thermal contraction during the experiment, the tubes are made to be of the same length and from the same material (stainless steel).
From a kinematics point of view the Film Aligner is similar to the flexible coupling. It consists of two pairs of pins. Each pair of pins is connected to a separate flexible clamp. Each of two samples (film/substrate or bulk) is squeezed between a respective pin pair and can be rotated around the pin-to-pin axis with a low predetermined friction. The clamp for the top sample is connected to the inner tube of the slider. The bottom sample clamp is connected to the outer tube. The rotation axes of the both samples are perpendicular to each other, in order that a full parallelism of their face surfaces can be achieved by bringing the films into contact for self-alignment.
The Coupling Probes are two half-wavelength antennas which provide contactless and variable coupling to the resonator.
During the measurement procedure, the samples are first pressed against each other for parallel self-positioning of their face surfaces. The sample is moved away from such contact up to 100-150 xcexcm separation with the 0.1-1 xcexcm increments. At each increment, measurements of the resonance frequency and Q-factor of the resonator vs. the separation value are made for further processing in accordance with theoretical formulas in order to extract the absolute values of xcex and RS, which may be further used to determine other parameters of the samples such as absolute complex conductivity surface impedance, etc.
These and other novel features and advantages of this invention will be fully understood from the following detailed description of the accompanying drawings.